### Course Syllabus

- First order equations.
- First order linear and nonlinear equations: analytic methods for solving linear equations, separable equations and exact equations.
- Modeling with linear first order equations: exponential growth and decay; mixing problems; interest rates; and others.
- Modeling with nonlinear first order equations, geometric methods and qualitative analysis, population models, phase portrait and classification of equilibrium points.

- Second order equations.
- Theory, linearity principle.
- Homogenous second order linear differential equations with constant coefficients. Real, complex roots, and repeated roots.
- Inhomogeneous second order linear differential equations: methods of undetermined coefficients.
- Modeling with linear second order equations: Mechanical and electrical oscillations. Forcing and resonances.

- Laplace transform methods.
- Laplace transform for initial value problems.
- Discontinuous forcing.
- Impulse functions and convolutions.

- Systems of linear differential equations: eigenvalues and
eigenvectors, phase portraits.
- Review of linear algebra: matrices, eigenvalues and eigenvectors.
- System of linear equations with constant coefficients: solving initial value problems with real and complex eigenvalues.
- Classification of equilibrium points, sinks, sources, saddles, centers, spiral sinks and spiral sources.

**Elementary Differential Equations**, 11th edition, by
*Boyce, DiPrima and Meade*.